Trunking system



March l0, l925.

R. M. FOSTER TRUNKING SYSTEM Filed Feb.

26, 1921 2 Sheets-Sheet l 3mm/Lto@ dll/Favier March l0- 1925.

R. M. FOSTER TRUNKING SYSTEM Filed Feb. 26, 1921 2 Sheets-Sheet 2 www/-Mwe EFM@ Patented Mar. 10, 1925.

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AND .TEDEGBAPH COMPANY,A A JCORPORALTIN NEWl` YORK-.J

TRUNKING SYS'TliEllLlSJ.y

Application niearetrnary 26,1921. seriamv: 445056.

T allmiuhmn` t may concer/nz' Be it known that LR'oNALD ITKOSTER, y,

residing at Brooklyn, in the' county of Kings and State of New"York,have inventedcerl tain 'Improvements .ini TrunkingfSystems,

or" which thefollov'vingnisal specification."

"This invention relates to signalingcircuits and more particularlyjtomethods'and means for trunking between different subi 1.0 scribers'in atelephone/exchange orbetween subscribers in differentexchanges.y

He'retofore in" providing Y trunking arrangements for handling the.traic origi-l nated by.v subscribers lines,-V particularly where" theconnections were established' `by means of switching machinery,` two'general inethodshave been proposed. O'ne method involved `providing'asuflicient rnumberl of trunks'to handle all ofthe trallic originated"method 'is' subject'tof the disadvantage, however, tlrat while.economic' inthe ImatterV of switching arrangements: or machinery itil isprodigal intheuse ofk trunks, since the total number oftrunksf'requir'ed 'to handlethe traffic lfrom .all of' the subscribersisgreater v.than .would be thecase in the irst method' referred' to above,du'e to the" factthat` the ratio of'ftrunks .td subscribers "variesinversel7 .witl'i'th number'of subscribers having access to the trunks.

It is one. of the'principal objects orV the presentlinvention `toprovide a scheme for multipling trunks such thatV thense of switcheshaving a small `number of switching points will be permitted withoutrequiring a large ratio 'of "thetotal num-ber of ftrunks to the' total"number' of's'ubscribers;

yThe above object, as well'ias other objects "by thes'ubscribers lines'involved" and es-` number of selectin@- points corresponding tokthenumber'ol'trun is 'necessary to handle'the traffic.

"in the group.

The first ofA these methods-possessesthe The other methodv consistsin-'divid ing the subscribers lines into groupsjand" providing trunksfor each group sufficient in number to handle the trafiic' originatingadvairtage'that the number of trunksk neces-k large probability of aAcall beinglostfdue serious disadvantage, however, that each subscribermust have l available a switching arrangement having a number ofswitching to all of the trunksfbeing busy will be a minimum. `The methodis subject to the'A 4o `vterminal's suliicient to 4connect with 'eachCand allof the trunks,iand where ythetraffi'c is so large as' to requirea :great number; of trunks 1 hating in each gro-upwillbe"Within"tthe'capacity limits of a relatively small and inexpensiveswitching arrangement; that is, a switching arrangement: havingacomparay, more Yfullr .a earinof hereinafter i are kactablishin-gconneotionsfbetween the calling 5 Pp l" subscribers lines and the`trunks through' a switcliingi arrangement equipped with a complished'byi the use ofawhat Sis herein termed a random slip,a multiple.Tlienature of'this multiple will `now be clear .from

the followingdescription ofthe invention, y

wheny read in connection with theac'companying drawing, Figure' l fofwhich" 1s a 1schematic diagram of Ia soc'alled straight multiple, Figs.2 and 3y inclusive, of which are `schematic diagramsof a trunking systemvin which" the multiples are"slipped upc-n a purely random' basis; whileFig.V 4

is a schematic diagram lof a modification in which.'` the slipping4 of`y the multiple is worked' out in 'accordance with' a Adefinite lawwhich closely approximates theu conditionsinvo'lv'ed in a perfectran-domslip."

In ordertofunderstand tlieprincipleunderlying a lrandom slip multipleIctus consider, for. example,v a group "of 100 trunks Ycarrying the'traffic originated by subscribers` lines.` Assume that eachsubscribersline is equipped 'witlia "100 point selector,

thereby" giving each" linev access" to the Yentire trunks. VLet'tlie`order in which v*the trunks are connected to the different selectors bevaried as much. as possiblev A perfectly heterogeneous arrangement wouldbe onesuch that when 37 (for'ex'ample)` of the trunks are as likely tobe the trunks-actually advantages previously discussed. Let us nowcalculate for such a promiscuously7 connected multiple the probabilitythat more than 20 terminals (for example) will have to be hunted over bya selector before an idle trunk is obtained. The load to be earried maybe adjusted so that the probability comes ont any desired value as. forexample .001. It is evident that under these conditions the last 80terminals ot every group may be disconnected from the trunks withoutappreciably changing the eiiiciency ot the group of 100 trunks.Consequently each partially wired selector may be replaced by a 20 pointswitch having access to the same trunks in the same order as the {irstQ0 trunks hunted over by the corresponding 100 point selector. Such anarrangement will involve what is herein termed a random slip multipleand has the obvious advantage that a 20 point switch may be used havingaccess to 20 trunks previously selected at random trom the total numberot trunks without increasing the total number ot trunks required tohandle the traiiie from all ot the subscribers.

Considering the saine arrangement trom another view point, assume 5independent groups ot lines equipped with selectors.` Let `each group otselectors be wired to a group of 9.0 trunks. The total number oi' trunkrequired will therefore be 100. li' we bring together these isolatedgroups oi' selectors and groups ot trunks by a partial interchange ottrunks, or in other words, by arranging matters so that each one ot the5 groups oi selectors exchanges some ot its trunks 'for some of thetrunks assigned to each ol the other 4v groups, we will. have apromiscuously connected multiple ot l00 rtrunks to some 20 of which eachselector will have access. .lt this interchanging were done thoroughlythe load carried by the total number of -trunks with a givenprobabilityT :o't' lost calls would be appreciably greater than the loadcarried by the same number oi: trunks when divided into live isolatedgroups each ot which is accessible to a 20 point selector.

In order that the advantages inherent in the random slip multiple may bemore apparent a mathematical solution oi' the problem involved willnowbe given. rThe problem may be stated as itollows:

A group of T trunks handles the tratlic originated by n sub-groiips oflines or switches.

Sub-group ,itl oit lines or switches has access to a specified number t1ot the T trunks.

Subgroup #2 of ylines or switches has access to a speciiied number t2 otthe T trunks. Some of these t2 trunks are not iiicluded in the l trunksassigned to subgroup #1.

Subgroup :#:3 ot lines or switches has access to a speciiied number t.;ot' the T trunks. Some of these t3 trunks are not included in the t1trunks assigned to subgroup .tz-"l and some are not included in the f2trunks assigned to sub-groiip #2. The trunks i. and t2 together may,however, include all the t., trunks.

Sub-group :tt/1i. ot lines or switches has access to a specitied numbert ot the T trunks. with either the t1, t2, t. or t-l trunks `but theyare all included in the totality oi tl-tetg-l- -l-tu-l trunks.

Thus, no sub-group of lilies or switches has the exclusive use ot a seto't trunks chosen from among the T trunks and on the other hand no twoor more. sub-groups use identically the same trunks. Y

lt is not assumed above that numerically tlztgztn: nml-tn although thiswill probably be the case in practice.

Such a group ot T trunks giving servcc to several over-lapping orinter-linking subgroups ot lines, each of which subgroups makes partialuse ot the T trunks`r may be defined as a random slip multiple providedthe 'following statement can be niade with reference to it when S ot theT trunks are busy they are as likely to be one speeii'ied set oi" Strunks as another specified set ot S trunks.

ln (.ider to solve this` problem let P. :probability that a subscriberoriginata call from a sub-group havin?.- access to a i' ot T trunkstails to get an idle truuk.

Assume that at the moment the call is made S ot the T trunks are busv.The probability of the existence ot this Lassumed condition is where Ais the average load arried bv the group T. i

rllhe probability that the assumed S busy trunks embrace the particulart trunks tio which the subscriber under consideration has access isTherefore, the compound probability that S of. the T trunks are busy andthat'these S trunks include the if trunks under consideration is Theset.. trunks are not identical;

Therefore l i A S=T 1,

nelg) (g-Srrrn) n :probabilitylnt all-Ttr-unks are busy. l

Now y l v T-i T-t-i gz lgm--mr-m) Therefore, finally, `t y y y KO y y yThe preceding equation gives the probability of lost calls in terms ofthe average ,load carried by the group of trunks, the total number oftrunks involved, and the number of trunks/assigned to each group. lViththis equation asa basis Tables I` and II have been prepared to show thesaving involved in a random slip multiple as compared with a straightmultiple, that is, a multiple in vwhich vthe trunks are divided intoindependent groups, Vea'eh group accessible to' a switch having acorrespondingly' smallnumber of terminal points.

In a system where 20 point sender seleo .tors give ac oessto the sendersof an` automatieI switching exchange the saving in senders when therandom slip arrangement is used instead of the. straight multiple willbe as indicated in Table I. It can be readily seen from the table thatwith the l random slip arrangement the number` ot senders required tocarry a given loadfis considerably smaller than the number ot sendersnecessary for the same load with.'

the r straight multiple. `For example, it`

` is apparent that if the allowable probability of lost calls is .O01and the trunks are dividedv into ten groups of 20eaoh the random slipmultiple arrangement Vwill require only 137 senders as against 200senders inquiredy by the straight multiple ar- `rangement for an averageload of 89.6, the

expression average load beinghere taken `to mean the average number ofconnections existing at any onetime for the entire group of trunks Thesaving just referred to amounts to 31.5%. On the other hand, in aueasewhere but one group is involved and the average load is 8.96, 20 senderswill be required in both' eases; and they random .46'

` slip multiple presentano advantages over Y Straight multiple.

the straight multiple, as in this limiting oase the random slipmultiplebeeomes a Table II shows the saving in fina-l switches whichwould result from a random arrangement of trunks to finals 1n a panelsys* tem where the incoming multiple is divided into groups of 24 trunkseach. Here also a smaller number of switches can carry the same load asa larger number with the straight multiple or inversely, the same numberof `switches in the random arrangement can take care of a larger loadthan in the straight multiple arrangement. f Table I.

j l Random l btnught multiple. umltipla y l Per cent Average load. y y lSwingin Number lotal Total senders.

0f You s senders senders ,i gl p required. requiredq 1 20 20 .f 04 .2ll() 34 i 15. 0 3 eo .471 21.7 4 S0 (i0 l 25.0 5 100 T. l 27. 0 l0 200137 3l. 5 l5 300 199 i 33.7 2O 400 262 .f 34.5 25 500 326 34. S

Tabla II.

Straight multiple.

i J UM Pereentl` Average load. saving in Egg? umher Total Total finals.y i ou s finals finals l gr p required. required.

I i l 1 241 24 o i 2 48 43 10.4 3 72 I eo m. 7 4 as i 7s 18.8 5 120 9620. 0

rangements involving' the random slip CFI principle may be embodied invarious forms. In Figs. 2 and 3 are shown perfect random slipspermutations of the numbersl, 2, 3 and 4, the permutations being shownin Fig. l, which illustrates in schematic form the permutations of fourtrunks taken four at a time in accordance with the first method outlinedat the beginning of this specification. In all three figures a group ofT24 trunks is shown, together with `a:24 sub-'groups of subscriberslines. Each sub-group is represented by one line equipped with aselector giving the line access to four trunks in the case of Fig. l,three`-trunks in the case of Fig. 2 and two trunks in the case of Fig.3. In Fig. I and the succeeding figures the arrows may therefore betaken to represent the wipers of the switches,each of which is availableto one or more subscribers and each switch having terminal points equalin number to the vertical lines connecting the arc of acirclerepresenting the contact points of the switch-with the horizontallines representing ythe trunks; The numbers below the arrowsrepresenting the wipers of the switch indicate the order in which theswitches obtain access to the trunks.

If, in the case of the arrangement of Fig. 1 a determination is made ofthe probability that more than 3 terminals will have to be hunted overby the selector before an idle trunk is obtained and it be found thatthis robability is withinthe allowable probaiiility of lost calls, theconnection leading to the last trunkkby each switch may be omitted fromthe switches in Fig. 1, in which case we get the perfect random sliparrangement of Fig. 2, which is based upon permutations of 4 trunkstaken 3 at a time.

Similarly, vif it be found that the allowable probability will permit ofdispensing with connect-ions to the last two trunks selected by eachswitch in Fig. 1, we may obtain the perfect random slip multipleillustrated in Fig. 3 which involves permutations of 4 trunks taken twoat a time.

The slip arrangements illustrated in Figs. 2 and 3 are based upon allpossible permutations of the numbers involved. Conse-v based on allpossible permutations, wherev the total number of trunks T is large. Forexample, a slip multiple of T:25 trunks, in which" each line is equippedwith a z5 point selector would require the lines to be divided. into 2524X23 22 2I:6,375,600 sub-'groups if every possible. permutation ofy\sub-' roup based on all of ther24 possibleU4 therefore becomesdesirable to devisea system in which only a part of all of the possiblepermutations will be used and in which thezse'lectcd permutations willbe so chosen that noparticular set of trunks is more likely to be busythan any other set involving the same number of trunks. In selecting alimited number of the .total possible permutations, `it is preferable toselect a minimum amount of overlapping i. e. permutations such-that anytrunk having a given number will appear in as few chosenA permutationsas possible.

Fig. .4 illustrates a practical form of slip arrangement obtained byfollowing the principles above discussed and in which a very thoroughintermixture of theI trunks is-obtained without dividing the lines intoan abnormal number of sub-groups. This figure illiistrates what isherein called a binomial slip arrangement as applied to a system,involvingl. trunks .and 5 poi-ntselectorsr In accordance with thisarrangement.l the trunks assigned to the first' sub-group of lines tothe left,.arethose havingY the binomial numbers l, 2, 4:22,' v8:23',.and 16:24. The numbers of the trunks to be assigned to the other groupsare. obtained by writing the numbers from 2 .to 17. as the numbers ofthe first trunks to be selected by the groups to the right of thathaving assigned to it the numbers l, 2,4 etc.v Similarly the numbersofthe second set of trunks to be selected is obtained bywritingsuccessive numbers beginningv with '3, while the numbers of thethird set are .obtained by writing successive numbers beginning with 5,etc. In Veach instance, whenthe number 17 is reached the-succeeding'number will be 1. An analysis of. this trunking. arrangement shows thatwhileit is not a perfect random slip arrangement, it conforms. very'closely to the requirements` of the random slip multiple.

It will be obvious thatthe'lgeneral principles hereinA disclosed `maybeembodiedin many other organizations,widely different from those-illustrated, without departing from the spirit of the invention asdefined in Y the? following claims.

`What is-claimed is:

l. A trunking system in which a plurality of trunks are provided forhandling vthe calls originating from all-of the subscribers linesinvolved, the subscribers-lines bel ing divided into sub-groups eachhaving access to a number of trunks lessv than `the total numberprovided, the .trunks vassigned to theseveral sub-groups beinginterchanged so that the sub-groupsoverlap .each other, the `numbers ofthe trunksassignedtofthe firstv sub-group and .the order .of-selectionthereof.v being obtained by: assigning to. said trunksv having r.' the'i, binomial num ers l, 2, 4:22 etc.,.and the' numbersof lll) the trunksassigned to the other sub-groupsy and the order of selection thereofbeing obtained by addingk successive numbers to the numbers assigned tothe irstfsub-group.

2. A trunking system in which a plurality of trunks gives service-toseveral overlapping and 'inter-linked' sub-groups of lines, eachsub-group of klines having access to a partvonly of the total number oftrunks, the

numbers of the trunks assigned to the first sub-group being obtained byassigning to said sub-group the binomial numbers 1, 2, 4:22 etc., andthe` numbers of the trunks assigned to the other sub-groups beingobtained by adding successive numbers to the numbers assigned to thefirst sub-group.

3. A trunking system in which ka plurality of trunksl gives service toseveral over-lapping and inter-linked sub-groups of lines, eachsub-group of lines having yaccess to a part only of the total number oftrunks, the

numbers of the trunks assigned to the first sub-group and their order ofselection being obtained by assigning to said sub-group the trunkshaving the binomial numbers 1, 2, 4:22 etc., and the numbers of thetrunks assigned to the other sub-groups and their order of selectionbeing determined by as-v signing to the other sub-groups trunks whosenumbers are obtained by adding successive numbers to the numbersassigned to the iirst sub-group, whereby When a given number of thetotal number of trunks are busy, the probability of one set of trunks ofthe given number being busy Will be substantially the saine as thevprobability that any other set of equal number Will be busy.

In testimony whereof, I have signed my name to this specification this23rd day of February, 1921.

RONALD M. FOSTER.

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